B. Tech in Instrumentation & Control Engineering
Nirma University Institute of Technology Department of Instrumentation and Control Engineering B Tech in Instrumentation and Control Engineering 1 | P a g e MA101: Calculus [3 1 0 4] Learning outcomes: On completion of the course student CLO1: will be able to find higher ordered derivatives and hence represent function in power series of (x-a) CLO2: will apply the knowledge of function of several variables , its derivatives in engineering problems CLO3: will apply the knowledge of special functions(Gamma, Beta, Elliptic, Error) and its application in engineering problems CLO4: will apply the knowledge of multiple integration and its application in engineering problems Syllabus: Unit I: Differential Calculus Review of limits, continuity and differentiability, Successive differentiation, Leibnitz theorem (without proof), Indeterminate forms, Taylor’s and Maclaurin’s expansion of single variable, Partial Differentiation, Total derivative, Chain Rule, Implicit function, Euler’s theorem and its applications, Taylor’s and Maclaurin’s expansion of function of several variables, Maxima and Minima of function of several variables, Lagrange’s method of undetermined multipliers, Jacobian. Unit II: Integral Calculus Review of proper and improper integrals, Reduction formulae, Beta-Gamma functions, Error function, Tracing of curves, Rectification, Quadrature, Volume of solid of revolution, Area of surface of revolution, Double integral and evaluation, Change of order of integration, Change of variable, Triple integral and evaluation, Area using double integration, Volume as double and triple integration, Volume of solid by double integration. References: 1. Thomas’ Calculus(Latest edition), Pearson publication. 2. G B Thomas and R. L. Finney, Calculus and Analytic Geometry (Latest edition), Narosa Publication, Delhi.
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